1. March 3, 2009Tom Gaisser1 Neutrino oscillations Review of particle physics, neutrino interactions and neutrino oscillations

2. March 3, 2009Tom Gaisser2 How particles interact Force carrier Particle 1 Particle 2 Elementary particles are point-like (without structure) Ordinary matter is composite and is mostly empty space proton = { u u d } neutron = { u d d } nucleus = collection of protons and neutrons ~10 -13 cm = 1 fermi (fm)

3. March 3, 2009Tom Gaisser3 Different kinds of interactions All electrically charged particles interact by exchanging photons. Photons are massless so force is long range. Protons and nuclei interact strongly via gluons. In quantum chromodynamics (QCD) the elementary constituents are quarks which are confined to a scale of 10 -13 cm = 1 fermi ħc / 1 fm ~ 0.2 GeV Neutral leptons (neutrinos) interact by exchanging a very heavy W boson. proton W boson neutrino muon Neutrinos interact very weakly because they have to exchange a very heavy W (or Z) boson.

4. March 3, 2009Tom Gaisser4 Neutrino interactions Particle charges ⅔ -⅓ 0 Force carrier charges 0 ±1 Example:  + decay u d  +  W+W+ Example:  + proton   + n  + Proton  ++ u d

5. March 3, 2009Tom Gaisser5     e e  e  p  W+W+ + +  e + e Introduction to High Energy Physics D.H. Perkins 3 rd edition (1987) 

6. March 3, 2009Tom Gaisser6 CKM Matrix Gives coupling of W ± to quarks –Unitary matrix Vij – V ud ~ V cs ~ V tb ~ 1 > V cd ~ V us ~ 0.23 >> V cb ~ V ts ~ 0.041 >> V ub, V td ( Cabibbo, Kobayashi, Maskawa )

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10. From Todor Stanev’s class February 26

11. March 3, 2009Tom Gaisser11 Atmospheric neutrinos Produced by cosmic-ray interactions –Last component of secondary cosmic radiation to be measured –Close genetic relation with muons p + A   ± (K ± ) + other hadrons  ± (K ± )   ± +  (  )  ±  e ± +  (  ) + e ( e ) e  e  p  

12. March 3, 2009Tom Gaisser12 Historical context Detection of atmospheric neutrinos Markov (1960) suggests Cherenkov light in deep lake or ocean to detect atmospheric interactions for neutrino physics Greisen (1960) suggests water Cherenkov detector in deep mine as a neutrino telescope for extraterrestrial neutrinos First recorded events in deep mines with electronic detectors, 1965: CWI detector (Reines et al.); KGF detector (Menon, Miyake et al.) Stability of matter: search for proton decay, 1980’s IMB & Kamioka -- water Cherenkov detectors KGF, NUSEX, Frejus, Soudan -- iron tracking calorimeters Principal background is interactions of atmospheric neutrinos Need to calculate flux of atmospheric neutrinos Two methods for calculating atmospheric neutrinos: From muons to parent pions infer neutrinos (Markov & Zheleznykh, 1961; Perkins) From primaries to , K and  to neutrinos ( Cowsik, 1965 and most later calculations) Essential features known since 1961: Markov & Zheleznykh, Zatsepin & Kuz’min Monte Carlo calculations follow second method

13. March 3, 2009Tom Gaisser13 Historical context (cont’d) Atmospheric neutrino anomaly - 1986, 1988 … IMB too few  decays (from interactions of  ) 1986 Kamioka  -like / e-like ratio too small. Neutrino oscillations first explicitly suggested in 1988 Kamioka paper IMB stopping / through-going consistent with no oscillations (1992) Hint of pathlength dependence from Kamioka, Fukuda et al., 1994 Discovery of atmospheric neutrino oscillations by S-K Super-K: “Evidence for neutrino oscillations” at Neutriino 98 Subsequent increasingly detailed analyses from Super-K:    Confirming evidence from MACRO, Soudan, K2K, MINOS Analyses based on ratios comparing to 1D calculations Compare up vs down Parallel discovery of oscillations of Solar neutrinos Homestake 1968-1995, SAGE, Gallex … chemistry counting expts. Kamioka, Super-K, SNO … higher energy with directionality e  ( ,  )

14. March 3, 2009Tom Gaisser14 Atmospheric neutrino beam Cosmic-ray protons produce neutrinos in atmosphere  / e ~ 2 for E < GeV Up-down symmetric Oscillation theory: –Characteristic length (E/  m 2 ) –related to  m 2 = m 1 2 – m 2 2 –Mixing strength (sin 2 2  ) Compare 2 pathlengths –Upward: 10,000 km –Downward: 10 – 20 km P(   ) = sin 2 2  sin 2 1.27 L(km)  m 2 (eV 2 ) E (GeV) () e  e  p  

15. March 3, 2009Tom Gaisser15 Classes of atmospheric events Contained (any direction) -induced  (from below) e (or  )   Contained events

16. March 3, 2009Tom Gaisser16 Super-K atmospheric neutrino data (hep-ex/0501064) 1489day FC+PC data + 1646day upward going muon data CC e CC 

17. Atmospheric Flavor state |  ) =  i U  i | i ), where | i ) is a mass eigenstate 10 0 0 C 23 S 23 0 -S 23 C 23 C 13 0 S 13 0 1 0 -S 13 0 C 13 C 12 S 12 0 -S 12 C 12 0 0 0 1 U = “atmospheric” “solar” C 13 ~ 1 S 13 small   ,  m 2 = 2.5 x 10 -3 eV 2 maximal mixing Solar neutrinos e  { ,  },  m 2 ~ 10 -4 eV 2 large mixing 3-flavor mixing Yumiko Takenaga, ICRC2007

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